I don't know what it's like in DC, but in my city the worst districts have to pay quite a bit more for personnel (teachers, admin, substitutes, everyone) and st

I don't know what it's like in DC, but in my city the worst districts have to pay quite a bit more for personnel (teachers, admin, substitutes, everyone) and still don't usually attract the best, because working in a place with multiple violent disruptions in each classroom every week and where the 2nd graders yell at their substitutes and call them names that 2nd graders ought not know is frustrating and dangerous. It's way easier to feel like you're effective and appreciated in the good districts, even if you're making 20% less. If DC paid the national average it's possible no one would work there, not even mediocre teachers. So yeah, there may tend to be an inverse relationship between spending and quality, but it's (likely, in most cases) not that the money is causing the problem but rather that the problem is forcing more spending just to tread water, let alone improve anything.